We study the effects that the gravitational interaction of f(R) theories of
gravity in Palatini formalism has on the stationary states of the Hydrogen
atom. We show that the role of gravity in this system is very important for
lagrangians f(R) with terms that grow at low curvatures, which have been
proposed to explain the accelerated expansion rate of the universe. In fact,
new gravitationally induced terms in the atomic Hamiltonian generate a strong
backreaction that is incompatible with the very existence of bound states. The
universe that we observe is, therefore, incompatible with that kind of
gravitational interaction. Lagrangians with high curvature corrections do not
lead to such instabilities.

I've been curious about this paper for a little while. It purports to show that Palatini theories of gravity where f(R) includes a 1/R term are incompatible with the universe we live in, by looking at their effects on the hydrogen atom.

The basic claim is that in any such theory of gravity, the various curvature terms will modify gravity on all scales, and thus we cannot simply look at the effects of Palatini theories on large scales, but also small scales. The author then goes to show that when applied to the hydrogen atom, one finds that the mass changes depending upon whether the electron is in an orbital versus when it is unbounded, which provides a 'way out' of the electron via tunneling. This, therefore, makes the hydrogen atom unstable, which is clearly incompatible with observed reality.

So, my question is, does anybody here with more expertise in this area than myself know whether this paper is any good or not? It seems like, if correct, it could be very strong evidence in favor of dark energy as opposed to modified gravity.